I think I would simplify the application of the chain rule a bit by first writing the expression as:
Now, the derivative of the constant is zero, so we are left with:
See if you can now apply the rule:
As some added context, I am taking Calculus: Early Transcendental Functions and we are studying "The Natural Logarithm as an Integral"
The problem presented is as follows:
d/dx [ln (x^{5} sin x cos x)]
I've read through the material and even looked at some of the odd numbered problems that have answers but I just can't seem to get started here. Any advice on how to approach this?
I think I would simplify the application of the chain rule a bit by first writing the expression as:
Now, the derivative of the constant is zero, so we are left with:
See if you can now apply the rule:
Let's take a look at both approaches:
My approach:
Prove It's approach:
My approach has a more difficult application of the chain rule, but no need to apply double-angle identities (at least if you wish to combine the two trig. terms).